How do I remove these black pixels from my baked texture?
I think this is directly dependent of the texture size here.

There is no light under the cross, so there are blacks pixels to write on the texture. Here one pixel of the texture is a bit larger than the cross, so we can see these black pixels.

This can also appears when you're at the border of an uv island, if you don't activate the margin option in the baking panel, but it's not the case here.